pcieluck got it wrong. Osmosis works the opposite as described. When a cell is in a saline solution, the cell strives to achieve a balanced concentration of salt inside and outside. The cell pumps water OUT of the cell to balance it's internal salt with the outside salt. The concentration rises because there is less water in the cell than before. The concentration in the liquid drops because it gains water.
Osmosis is a special case of diffusion and just about every cook I hear mention "osmosis" gets it wrong. If Osmosis worked as described above post, swimming in the ocean would kill us as our body sucked up salt. A shower or bath would make us sick as our cells pumped out our electrolytes.
Now, Brining tends to add in the neighborhood of 10% weight to a brined product. That extra weight is retained interstitial brine/cellwater from standard diffusion. It's not retained in the cells. One thing both koshering and brining do is that the salt denatures protein a bit. This creates a bit of a gel quality in the liquid helping hold the extra liquid within the interstitial structure.
With your soup situation, you will need to hold very constant temps as a standard simmer, or even a boil will be too hot for your desired results. Proteins contract as they cook. You can watch a steak or any cutlet or burger pull together when it hits a hot pan for example. As proteins contract, they start to squeeze and wring out the moisture from the meat. So you'll need to hit a lower temp and hold it or you'll squeeze out the added salt water you brined into your chicken.
You might be better served making the soup as you would normally, then gently poach some other brined chicken in the finished stock. That would double your meat cost though.
The brine you describe in your first post is quite weak (low concentration), even for overnight use. Where you're trying to hit a specific salinity throughout, you'll need a longer time and probably smaller pieces.
The purply/brown areas you note are most likely from bone adjacent parts of the dark meat. Lots of free proteins (myoglobin) in those colored sections which are probably blocking the solution from penetration as they denature and gel up preventing the brine from penetrating. This comes from the young age at which chickens have been bred to be at slaughterable size. The leg bones are still quite porous at this age giving the discoloration you're seeing.